The Sixty-Pair Cycle (60 Gapja): A Table and How to Read Stem-Branch Names

How to read a stem-branch pair

A stem-branch name (간지) is a heavenly stem and an earthly branch placed one above the other. For 丙午, 丙 on top is the stem and 午 below is the branch, and when reading it the stem comes first: "byeong-o" (병오). Every pillar of a saju, every year and every day of the calendar is written as such a pair. The meaning of each stem and branch is covered in the "Heavenly Stems and Earthly Branches" article; this article deals with the 60 combinations made by pairing them.

When interpreting a pair, the yin-yang and element of both characters are considered together. 丙 is yang fire and 午 is also yang fire, so 丙午 is a pair that is fire both above and below. In 丁未 the top is yin fire and the bottom is yin earth, so it takes the form of fire giving birth to earth. In other words, even the same fire takes a different shape of energy depending on the branch it is paired with.

There is also a habit of naming years by turning the element of the stem into a colour and the branch into an animal. Wood is blue-green, fire is red, earth is yellow, metal is white and water is black. So the 丙午 (byeong-o) year 2026 is "the Year of the Red Horse" and the 丁未 (jeong-mi) year 2027 is "the Year of the Red Goat." These colour names are not part of a reading; they are nicknames added to make the years easy to call.

The table of 60 gapja

Stepping through the ten stems and twelve branches together, one at a time, gives the pairs 甲子, 乙丑, 丙寅 … in order, and after the 60th, 癸亥, it returns to 甲子. A yang stem meets only a yang branch and a yin stem only a yin branch, so pairs such as "甲丑" or "乙子" do not exist. In the table below the elements are in stem · branch order, and each year runs from Ipchun (입춘) to just before the next Ipchun.

Working out the stem-branch of a year

If you know the year, you can find its stem-branch by hand. The stem is set by the last digit of the year; there are ten stems, so the same stem comes round every 10 years. The branch is set by the remainder when the year is divided by 12. Below is the correspondence table taken from Halmeoni's calculation.

• Last digit of the year → stem: 0 庚, 1 辛, 2 壬, 3 癸, 4 甲, 5 乙, 6 丙, 7 丁, 8 戊, 9 己
• Remainder of year ÷ 12 → branch: 0 申, 1 酉, 2 戌, 3 亥, 4 子, 5 丑, 6 寅, 7 卯, 8 辰, 9 巳, 10 午, 11 未

For 2027, the last digit is 7, so the stem is 丁; 2027 divided by 12 leaves 11, so the branch is 未. Put together it is 丁未 (jeong-mi), number 44 in the table of 60 gapja. To get the number in one step, subtract 4 from the year, divide by 60, and add 1 to the remainder. The remainder of (2027 − 4) ÷ 60 is 43, so it is number 44. The 4 is subtracted because the year 4 CE was a 甲子 year. By the same method 2026 is number 43, 丙午.

This calculation is correct as it stands only for people born after Ipchun. If you were born in January or early February, before Ipchun, use the stem-branch of the previous year. The day on which the year and month change is covered in detail in the article "The 24 Solar Terms and the Month Pillar: The Day the Month Changes".

The same 60 gapja for months, days and hours

The 60 gapja are used for more than years. Months also follow the 60 gapja order, so the same pair comes round every 60 months, that is, every 5 years. The 寅 month of 2027 is 壬寅, and the 寅 month of 2032, five years later, is also 壬寅. Days come round every 60 days. 4 February 2027 is a 甲寅 day, and 5 April, 60 days later, is also a 甲寅 day. The day pillar uses this day's stem-branch as it is, so it is hard to find by hand without a manseryeok. Hours come twelve to a day, so 60 slots make one full round in five days.

The 60 gapja of years and days continue without a break, whereas the stems of months and hours are each set from the stem of that year and that day. That is why people born on the same day have the same day pillar, and people born in the same year between the same two solar terms have the same month pillar.

Ten-pair groups (순, 旬) and the Void (공망)

Cutting the 60 gapja into groups of ten, each beginning with 甲, gives six groups, and each group is called a ten-pair group (순, 旬). 甲子 to 癸酉 is the 甲子 group, and 甲戌 to 癸未 is the 甲戌 group. In one group all ten stems appear once each, but only ten of the twelve branches appear. The two branches left over without a partner are called the Void (공망, 空亡) of that group. The 甲子 group does not contain 戌 and 亥, so its Void is 戌亥.

Void means "an empty place," and it is read as a place where things are harder to hold on to than you intend. Which pillar's stem-branch is used to fix the Void differs from school to school. Many use the day pillar, and some also look at the year pillar. Halmeoni fixes the Void by the group that the day pillar belongs to, and checks whether the branches of the other pillars match those two characters. For example, if the day pillar is 甲寅, it belongs to the 甲寅 group, so the Void is 子丑.

The zodiac animal and the year stem are different

The zodiac animal (띠) is the lower character of the year pillar, the year branch (연지), named as an animal. There are twelve branches, so the animal comes round every 12 years. But the year pillar also has an upper character, the year stem (연간), and there are ten stems, so it comes round every 10 years. The pair made of the two comes back identically only after 60 years, the least common multiple of 12 and 10. Even among people born in Horse years, the year stem differs depending on the year of birth.

• Year pillars of Horse years: 1966 丙午, 1978 戊午, 1990 庚午, 2002 壬午, 2014 甲午, 2026 丙午

Those born in 1966 and 2026 are both born in a 丙午 year, but a Horse born in 1978 is 戊午 and one born in 1990 is 庚午. If the year stem is different, the relation to the Day Master (일간), that is, the Ten Gods (십신), is different. This is why a reading that speaks of a person by the animal alone is bound to be rough. Halmeoni uses the animal only in readings that take the animal as their basis, such as the Twelve Spirits (12신살) and the New Year fortune by animal, and when reading the whole saju it looks at the year stem and year branch together with the other six characters.

The year in which the stem-branch of your birth year returns for the first time is the hwangap (환갑). For someone born in the 丙午 year 1966, the 丙午 year 2026 is the hwangap, and for someone born in the 丁未 year 1967, the 丁未 year 2027 is the hwangap.

There is also a system called napeum (納音), in which the 60 gapja are grouped two at a time and given names that include an element, such as haejunggeum (해중금, "metal in the sea") for 甲子 and 乙丑. It is used in compatibility readings and older interpretations, but Halmeoni's calculation does not include napeum, so it is not listed in this table either.